Diophantine approximation in metric space
Copyright policy )Diophantine approximation in metric space
AbstractDiophantine approximation is traditionally the study of how well real numbers are approximated by rationals. We propose a model for studying Diophantine approximation in an arbitrary totally bounded metric space where the rationals are replaced with a countable hierarchy of “well‐spread” points, which we refer to asabstract rationals. We prove various Jarník–Besicovitch type dimension bounds and investigate their sharpness.
- University of St Andrews United Kingdom
- Wesleyan University United States
- University of Bristol United Kingdom
MCC, Mathematics - Number Theory, T-NDAS, Metric theory of other algorithms and expansions; measure and Hausdorff dimension, Hausdorff dimension, Jarník-Besicovitch theorem, 004, 510, abstract rationals, Fractals, Hausdorff and packing measures, Mathematics - Classical Analysis and ODEs, Diophantine approximation, Metric theory, Classical Analysis and ODEs (math.CA), FOS: Mathematics, QA Mathematics, Number Theory (math.NT), QA, Dirichlet spectrum
MCC, Mathematics - Number Theory, T-NDAS, Metric theory of other algorithms and expansions; measure and Hausdorff dimension, Hausdorff dimension, Jarník-Besicovitch theorem, 004, 510, abstract rationals, Fractals, Hausdorff and packing measures, Mathematics - Classical Analysis and ODEs, Diophantine approximation, Metric theory, Classical Analysis and ODEs (math.CA), FOS: Mathematics, QA Mathematics, Number Theory (math.NT), QA, Dirichlet spectrum
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